Labor has rejected demands for amendments to the cross-party same-sex marriage bill, with Mark Dreyfus saying the bill is already a compromise and Louise Pratt warning MPs on both sides to respect the postal survey result.

The Liberal senator David Fawcett told Guardian Australia that conservatives had dropped the suggestion commercial service providers, such as florists and bakers, should be allowed to refuse same-sex weddings but would propose other elements of the James Paterson bill as amendments.

While public advocacy of amendments has been limited to Coalition figures, the Labor senators Jacinta Collins, Deborah O’Neill, Chris Ketter, Alex Gallacher and Helen Polley, and MP Anthony Byrne, have all refused to say how they will vote, despite the 61.6% victory for the yes campaign in the postal survey. The Labor senator Don Farrell has said he will vote against same-sex marriage.

Philip Ruddock to examine if Australian law protects religious freedom

On Thursday Pratt told Guardian Australia that Labor had “a strong tradition of standing up for anti-discrimination law”.

Asked how her colleagues should exercise their conscience vote on the bill and amendments, she replied: “I call on all MPs to respect the outcome of the postal survey.

“We cannot entrench discrimination in the Marriage Act – it would be completely contrary to the outcome that the Australian community has asked for.”

Pratt noted a federal law giving parents the right to pull their children out of class might be unconstitutional because it is not sufficiently connected to marriage to come under the commonwealth’s head of power.

“We need to think very carefully before we give parents the right to interfere in secular education,” she said. “For example should we give parents the right to withdraw children from a science class because they believe in creationism?”

Fawcett said that different states and territories had inconsistent discrimination laws and the exemptions that religious organisations have to the federal Sex Discrimination Act should apply nationwide.

Fawcett backed Morrison’s position that no detriment clauses and freedom of speech provisions to prevent people from “harassing or threatening” others with traditional marriage views should be pursued regardless of the Ruddock review.

Earlier Dreyfus, the shadow attorney general, told ABC Radio: “We don’t think that anything should happen which gets in the way of marriage equality being made a reality in Australia by the end of this year.

Responding to Morrison’s claims that more religious protections were needed to represent the minority who voted against same-sex marriage, Dreyfus replied: “This is a bill for 100% of Australians.

“We are all better as a result of equality being given to all Australians.”

Dreyfus said the cross-party bill was “what we should be working on” and labelled proposed amendments to the cross-party bill “really peripheral matters or digression from the main issue”.

“It would be immensely disappointing not just to me but for many other Australians if the removal of discrimination, which is what marriage equality is about, was seized on as an opportunity to actually increase discrimination,” he said.

He said the appointment of Philip Ruddock and others to a separate religious freedom inquiry was a “thoughtful approach”.